Matrix-Based Computational Method for Upper and Lower Approximations of Rough Sets
Tianrui Li · 2011
The concepts of an induced matrix of equivalence relation matrix and a λ-cut matrix of matrix are introduced on the basis of Boolean column matrix representation of subsets in the universe.Then,a matrix method for computing upper and lower approximations of a concept in Pawlak rough set model is proposed,which means the upper and lower approximations of a subset can be derived from the operation among the Boolean column matrix of the subset,the equivalence relation matrix of the universe and the induced matrix.The correctness of the proposed method is proved.In addition,an algorithm for computing upper and lower approximations of a subset by the proposed method is given.Furthermore,the proposed method and its algorithm are generalized to compute upper and lower approximations of a concept in variable precision rough set model.The vacancy on the computation of lower approximation is filled by the proposed method.Therefore,it unifies the two matrix-based methods for computing upper and lower approximations of a concept in Pawlak rough set model and variable precision rough set model.